Yvette Cooper, the shadow home secretary, has rejected a poll conducted by YouGov for the Times showing Jeremy Corbyn on course to win the Labour leadership election, with a 17-point lead ahead of the other candidates on first preference votes.

Cooper was the only Labour leadership hopeful so far to speak out against the findings of the YouGov poll, which is the first to be published since the leadership contest began and claims to be based on a sample of Labour members, registered supporters and union supporters. As well as a win for Corbyn (43%), the poll suggests Andy Burnham (26%) would come second, Cooper (20%) third and Liz Kendall (11%) fourth.

Polls of party members are difficult to conduct and the British Polling Council has yet to conclude its inquiry into how the pollsters managed to get the general election result wrong.

But the poll, in the absence of any other data beyond constituency and union nominations, will send shockwaves through a party establishment that never thought Corbyn’s brand of anti-austerity politics had a chance of winning.

The poll, which predicts Corbyn winning with 53% of the vote in a runoff against Burnham, questioned 1,054 people, of whom 20% have yet to decide how to vote.

The worry for the Cooper campaign is that the poll will suggest the contest will narrow to a battle between Corbyn and Burnham, viewed as the candidate closest to Corbyn.

A spokesperson for Cooper said: “This doesn’t reflect our internal data and significantly understates the huge number of members and supporters giving Yvette their first preference.

“However, what it does show is that Yvette is now the only candidate who can win the leadership election and then reach out to the wider electorate to win the general election in 2020. We won’t do that by shifting a narrow party further to the left or by returning to the dismal days of the 1980s, with internal party warfare and almost two decades of opposition.”

John McTernan, a former special adviser to Tony Blair in Downing Street, told the BBC’s Newsnight programme that the figures were disastrous. He suggested two of the frontbenchers should consider dropping out in order to pool centrist support and block Corbyn.

“These figures are disastrous for the Labour party, disastrous. The fact is the other candidates need to decide who is the ABC candidate – the Anyone but Corbyn candidate,” he said.

McTernan complained that party activists were “suicidally inclined” and condemned MPs who had “lent” their nominations to Corbyn in order broaden the debate, even though they did not want him as leader. “They need their heads felt,” he said. “They are morons.”

Tony Blair is due to address an event hosted by the Progress thinktank on Wednesday and is likely to repeat his warnings against a Labour lurch to the left. Before the general election, he cautioned that when a traditional leftwing party took on a traditional rightwing party it usually ended with a “traditional result” – a Tory victory.

On Tuesday, Burnham said the Labour party was “crying out for leadership” after it made a messof Monday night’s vote on the government’s welfare bill. He said that if elected leader this September, he would ensure that Labour opposed the government welfare bill outright and would expect all Labour MPs to do the same.

Speaking at a Co-op leadership hustings on Tuesday night, he said: “The last seven days have shown the depth of our confusion and the party is crying out for leadership. That is what I have shown in moving the party’s position on the bill so that we tabled an amendment opposing the bill.”

Labour’s acting leader, Harriet Harman, provoked fury within the party when she announced that its MPs should abstain, so expressing support for the government’s lowering of the household welfare benefit cap. Harman tried to quell a growing rebellion over the decision by tabling an amendment setting out why the party disagreed with the government’s proposed bill.

On Monday night, 48 Labour MPs, nearly a fifth of the parliamentary party, defied a three-line whip that ordered them to back an amendment rejecting the bill, but then to abstain on the bill’s second reading.

Burnham admitted the position adopted by the shadow cabinet had been messy, but it was the necessary price to secure a compromise inside the party. In remarks aimed at Corbyn, he said: “It is also leadership not creating a split in the party.”